Finding frequent patterns in a string in sublinear time

Abstract

We consider the problem of testing whether (a large part of) a given string X of length n over some finite alphabet is covered by multiple occurrences of some (unspecified) pattern Y of arbitrary length in the combinatorial property testing model. Our algorithms randomly query a sublinear number of positions of X, and run in sublinear time in n. We first focus on finding patterns of a given length, and then discuss finding patterns of unspecified length. © Springer-Verlag Berlin Heidelberg 2005.